Multiparticle collision dynamics simulations of a squirmer in a nematic fluid

We study the dynamics of a squirmer in a nematic liquid crystal using the multiparticle collision dynamics (MPCD) method. A recently developed nematic MPCD method [Phys. Rev. E 99, 063319 (2019)] which employs a tensor order parameter to describe the spatial and temporal variations of the nematic order is used to simulate the suspending anisotropic fluid. Considering both nematodynamic effects (anisotropic viscosity and elasticity) and thermal fluctuations, in the present study, we couple the nematic MPCD algorithm with a molecular dynamics (MD) scheme for the squirmer. A unique feature of the proposed method is that the nematic order, the fluid, and the squirmer are all represented in a particle-based framework. To test the applicability of this nematic MPCD-MD method, we simulate the dynamics of a spherical squirmer with homeotropic surface anchoring conditions in a bulk domain. The importance of anisotropic viscosity and elasticity on the squirmer’s speed and orientation is studied for different values of self-propulsion strength and squirmer type (pusher, puller or neutral). In sharp contrast to Newtonian fluids, the speed of the squirmer in a nematic fluid depends on the squirmer type. Interestingly, the speed of a strong pusher is smaller in the nematic fluid than for the Newtonian case. The orientational dynamics of the squirmer in the nematic fluid also shows a non-trivial dependence on the squirmer type. Our results compare well with existing experimental and numerical data. The full particle-based framework could be easily extended to model the dynamics of multiple squirmers in anisotropic fluids. Graphic abstract

The formation of viscous anisotropy in the asthenosphere and its effect on plate tectonics

<p>Developing an appropriate characterization of upper mantle viscosity structure presents one of the biggest challenges for understanding geodynamic processes in the upper mantle. This is because different creep mechanisms become activated depending on depth, accumulated strain, and applied stress, and other factors such grain size and anisotropic fabric can change as the deformation develops, changing the effective viscosity. Here we focus on the relationship between anisotropic fabric development and viscous anisotropy.</p><p>Under applied shear, olivine crystals, which form a large proportion of the asthenosphere, rotate towards the shear direction and accumulate a lattice preferred orientation (LPO) parallel to the macroscopic deformation. On a large scale, LPO can be observed through the propagation of seismic waves because of the anisotropic elastic properties of olivine. As olivine is anisotropic in its viscous properties, this developing texture within the asthenosphere can affect the macro-scale viscosity of the asthenosphere. This behavior has been detected in rock mechanics measurements on pure olivine aggregates, showing more than an order magnitude of viscosity change between shear parallel to the olivine aggregate’s LPO versus shear across this fabric (Hansen et al., EPSL 2016a, JGR 2016b).</p><p>Here, we use numerical models developed first in MATLAB and then implemented into the mantle convection code ASPECT. These models incorporate both anisotropic fabric development and anisotropic viscosity, both calibrated according to laboratory measurements on slip system activities of olivine aggregates (Hansen et al., JGR 2016b), to better understand the coupling between the large-scale formation of LPO textures and changes in asthenospheric viscosity.</p><p>The modeling results allows us to discuss the role of anisotropic viscosity on the processes of plate tectonics. An asthenosphere with a well-developed LPO becomes weak parallel to its texture, allowing for increasing plate velocity at the surface, for a given applied driving force.  On the other hand, this fabric resists abrupt changes in the direction of plate motion because the effective viscosity is elevated for shear perpendicular to the developed LPO. This increased resistance to fabric-perpendicular shear also decreases strain rates, which slows texture development. This means that asthenospheric fabric can impede changes in plate motion direction for periods of over 10 Myrs. However, the same well-developed texture in the asthenosphere could enhance the initiation of subduction or lithospheric gravitational instabilities as vertical deformation is favored across a sub-lithospheric olivine fabric, and the sheared fabric can quickly rotate into a vertical LPO. These end-member cases examining shear-deformation across a formed asthenospheric fabric illustrate the importance of olivine fabrics, and their associated viscous anisotropy, for a variety of geodynamic processes.</p>

Sound-wave instabilities in dilute plasmas with cosmic rays: implications for cosmic ray confinement and the Perseus X-ray ripples

ABSTRACT Weakly collisional, magnetized plasmas characterized by anisotropic viscosity and conduction are ubiquitous in galaxies, haloes, and the intracluster medium (ICM). Cosmic rays (CRs) play an important role in these environments as well, by providing additional pressure and heating to the thermal plasma. We carry out a linear stability analysis of weakly collisional plasmas with CRs using Braginskii MHD for the thermal gas. We assume that the CRs stream at the Alfvén speed, which in a weakly collisional plasma depends on the pressure anisotropy (Δp) of the thermal plasma. We find that this Δp dependence introduces a phase shift between the CR-pressure and gas-density fluctuations. This drives a fast-growing acoustic instability: CRs offset the damping of acoustic waves by anisotropic viscosity and give rise to wave growth when the ratio of CR pressure to gas pressure is ≳αβ−1/2, where β is the ratio of thermal to magnetic pressure, and α, typically ≲1, depends on other dimensionless parameters. In high-β environments like the ICM, this condition is satisfied for small CR pressures. We speculate that the instability studied here may contribute to the scattering of high-energy CRs and to the excitation of sound waves in galaxy-halo, group and cluster plasmas, including the long-wavelength X-ray fluctuations in Chandra observations of the Perseus cluster. It may also be important in the vicinity of shocks in dilute plasmas (e.g. cluster virial shocks or galactic wind termination shocks), where the CR pressure is locally enhanced.

Anisotropic viscoelastic phase separation in polydisperse hard rods leads to nonsticky gelation

Spinodal demixing into two phases having very different viscosities leads to viscoelastic networks—i.e., gels—usually as a result of attractive particle interactions. Here, however, we demonstrate demixing in a colloidal system of polydisperse, rod-like clay particles that is driven by particle repulsions instead. One of the phases is a nematic liquid crystal with a highly anisotropic viscosity, allowing flow along the director, but suppressing it in other directions. This phase coexists with a dilute isotropic phase. Real-space analysis and molecular-dynamics simulations both reveal a long-lived network structure that is locally anisotropic, yet macroscopically isotropic. We show that our system exhibits the characteristics of colloidal gelation, leading to nonsticky gels.

Generalized Navier–Stokes equations with nonlinear anisotropic viscosity

The purpose of this work is to study the generalized Navier–Stokes equations with nonlinear viscosity that, in addition, can be fully anisotropic. Existence of very weak solutions is proved for the associated initial and boundary-value problem, supplemented with no-slip boundary conditions. We show that our existence result is optimal in some directions provided there is some compensation in the remaining directions. A particular simplification of the problem studied here, reduces to the Navier–Stokes equations with (linear) anisotropic viscosity used to model either the turbulence or the Ekman layer in atmospheric and oceanic fluid flows.